In which of the following functions Rolle's theorem is applicable?
P
(a) \( f(x)=\left\{\begin{a...
In which of the following functions Rolle's theorem is applicable?
P
(a) \( f(x)=\left\{\begin{array}{lc}x, & 0 \leq x1 \\ 0, & x=1\end{array}\right. \) on \( [0,1] \)
W.
(b) \( f(x)=\left\{\begin{array}{ll}\frac{\sin x}{x}, & -\pi \leq x0 \\ 0, & x=0\end{array}\right. \) on \( [-\pi, 0] \)
(c) \( f(x)=\frac{x^{2}-x-6}{x-1} \) on \( [-2,3] \)
(d) \( f(x)=\left\{\begin{array}{cl}\frac{x^{3}-2 x^{2}-5 x+6}{x-1} & \text { if } x \neq 1 \\ -6, & \text { if } x=1\end{array}\right. \) on \( [-2,3] \)
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